Arithmetical properties of function fields (II). The generalized Schur problem
Michael Fried (1974)
Acta Arithmetica
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Michael Fried (1974)
Acta Arithmetica
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Santiago Boza, María Carro (1998)
Studia Mathematica
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We study various characterizations of the Hardy spaces via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.
Wang Yuan (1987)
Acta Arithmetica
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Carl Pomerance (1974)
Acta Arithmetica
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Richard Wheeden (1993)
Studia Mathematica
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A new characterization is given for the pairs of weight functions v, w for which the fractional maximal function is a bounded operator from to when 1 < p < q < ∞ and X is a homogeneous space with a group structure. The case when X is n-dimensional Euclidean space is included.
Charles Osgood (1974)
Acta Arithmetica
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P. Hitczenko, S. Montgomery-Smith, K. Oleszkiewicz (1997)
Studia Mathematica
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This paper gives upper and lower bounds for moments of sums of independent random variables which satisfy the condition , where are concave functions. As a consequence we obtain precise information about the tail probabilities of linear combinations of independent random variables for which for some fixed 0 < r ≤ 1. This complements work of Gluskin and Kwapień who have done the same for convex functions N.
E. Szemerédi (1974)
Acta Arithmetica
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Stefan Geiss (1997)
Studia Mathematica
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We investigate a scale of -spaces defined with the help of certain Lorentz norms. The results are applied to extrapolation techniques concerning operators defined on adapted sequences. Our extrapolation works simultaneously with two operators, starts with --estimates, and arrives at --estimates, or more generally, at estimates between K-functionals from interpolation theory.
Sandra Monteferrante, P. Szüsz (1970)
Acta Arithmetica
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Guozhen Lu, Richard Wheeden (2000)
Studia Mathematica
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We derive various integral representation formulas for a function minus a polynomial in terms of vector field gradients of the function of appropriately high order. Our results hold in the general setting of metric spaces, including those associated with Carnot-Carathéodory vector fields, under the assumption that a suitable to Poincaré inequality holds. Of particular interest are the representation formulas in Euclidean space and stratified groups, where polynomials exist and ...
S. Raghavan, S. Rangachari (1970)
Acta Arithmetica
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Steve Hofmann (1994)
Studia Mathematica
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We formulate a version of the T1 theorem which enables us to treat singular integrals whose kernels need not satisfy the usual smoothness conditions. We also prove a weighted version. As an application of the general theory, we consider a class of multilinear singular integrals in related to the first Calderón commutator, but with a kernel which is far less regular.